# Thread: Complex Contour Integration of Real Improper Integrals

1. ## Complex Contour Integration of Real Improper Integrals

Does any body know how to go about doing the following Integrals using complex contour integration (upper half semicircle contour):

1) Integrate from 0 to infinity 1/(2+x+x^3) dx

2) Integrate from 1 to infinity 1/(x*sqrt(x^2-1)) dx

2. ## Re: Complex Contour Integration of Real Improper Integrals

Integrals of Rational Functions

has everything you need to know.

you can search for "How to evaluate an improper integral with a contour integral." to skip directly to it.

3. ## Re: Complex Contour Integration of Real Improper Integrals

Thanks,much appreciated.

4. ## Re: Complex Contour Integration of Real Improper Integrals

I had a look at that site....very helpful,but the integral I posted: Integral 0 to infinity 1/(2+x+x^3) is an odd integrand,so cant use a semicircle contour.I couldn't find anything on that site when dealing with an odd integrand

What contour should I use for this problem? I have tried using a sector but couldn't get it to work...